Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory
Increasing the frequency range of physics-based predictions of earthquake ground motions requires to account for small-scale heterogeneities, which can only be described in a stochastic way. Although many studies have addressed the impact of random heterogeneities on ground motion intensity paramete...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-11-01
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| Series: | Frontiers in Earth Science |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/feart.2022.1033109/full |
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| author | Malcon Celorio Malcon Celorio Emmanuel Chaljub Ludovic Margerin Laurent Stehly |
| author_facet | Malcon Celorio Malcon Celorio Emmanuel Chaljub Ludovic Margerin Laurent Stehly |
| author_sort | Malcon Celorio |
| collection | DOAJ |
| description | Increasing the frequency range of physics-based predictions of earthquake ground motions requires to account for small-scale heterogeneities, which can only be described in a stochastic way. Although many studies have addressed the impact of random heterogeneities on ground motion intensity parameters obtained by numerical simulation, very few have verified the accuracy of their numerical solutions or controlled the scattering regime they were simulating. Here we present a comprehensive analysis of SH wave propagation in 2D random media which covers a broad range of propagation regimes from ballistic to diffusive. The coherent and incoherent parts of the wavefield are examined independently. The random media consist in correlated density and velocity fluctuations described by a von Kármán autocorrelation function with a Hurst coefficient of 0.25 and a correlation length a = 500 m. The Birch correlation coefficient which relates density to velocity fluctuations takes 4 possible values between 0.5 and 1, and the standard deviation of the perturbations is either 5% or 10%. Spectral element simulations of SH wave propagation excited by a plane wave are performed for normalized wavenumbers (ka) up to 5. Analysis of the decay of the coherent wave amplitude, obtained through different averaging procedures, allows for a direct measure of the scattering attenuation, which we successfully compare with the predictions of the Dyson mean field theory. We also present the comparison between the energy envelopes measured from the synthetics and their theoretical counterpart provided by the radiative transfer theory and the diffusion approximation. Excellent agreement is found between numerical simulations and theoretical predictions of radiative transfer theory for the mean intensity. The numerical study highlights the difference of attenuation length between the mean field and the mean intensity. In the forward scattering regime, the peak intensity appears to decay exponentially over a length scale known as the transport mean free path. Furthermore, the fluctuations of intensity in the ballistic peak exhibit a transition from Log-normal to Exponential statistics. This transition occurs for a propagation distance of the order of the mean free path, which offers an alternative method of estimating this parameter. |
| first_indexed | 2024-04-11T07:38:10Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2296-6463 |
| language | English |
| last_indexed | 2024-04-11T07:38:10Z |
| publishDate | 2022-11-01 |
| publisher | Frontiers Media S.A. |
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| series | Frontiers in Earth Science |
| spelling | doaj.art-1aa50db318e14c148534dd478447c92c2022-12-22T04:36:40ZengFrontiers Media S.A.Frontiers in Earth Science2296-64632022-11-011010.3389/feart.2022.10331091033109Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theoryMalcon Celorio0Malcon Celorio1Emmanuel Chaljub2Ludovic Margerin3Laurent Stehly4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, Univ. Gustave Eiffel, ISTerre, Grenoble, FranceGrupo Quimbaya, CEIFI, Observatorio Sismológico Universidad del Quindío, Armenia, ColombiaUniv. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, Univ. Gustave Eiffel, ISTerre, Grenoble, FranceInstitut de Recherche en Astrophysique et Planétologie, Observatoire Midi-Pyrénées, Université Paul Sabatier, CNRS, Toulouse, FranceUniv. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, Univ. Gustave Eiffel, ISTerre, Grenoble, FranceIncreasing the frequency range of physics-based predictions of earthquake ground motions requires to account for small-scale heterogeneities, which can only be described in a stochastic way. Although many studies have addressed the impact of random heterogeneities on ground motion intensity parameters obtained by numerical simulation, very few have verified the accuracy of their numerical solutions or controlled the scattering regime they were simulating. Here we present a comprehensive analysis of SH wave propagation in 2D random media which covers a broad range of propagation regimes from ballistic to diffusive. The coherent and incoherent parts of the wavefield are examined independently. The random media consist in correlated density and velocity fluctuations described by a von Kármán autocorrelation function with a Hurst coefficient of 0.25 and a correlation length a = 500 m. The Birch correlation coefficient which relates density to velocity fluctuations takes 4 possible values between 0.5 and 1, and the standard deviation of the perturbations is either 5% or 10%. Spectral element simulations of SH wave propagation excited by a plane wave are performed for normalized wavenumbers (ka) up to 5. Analysis of the decay of the coherent wave amplitude, obtained through different averaging procedures, allows for a direct measure of the scattering attenuation, which we successfully compare with the predictions of the Dyson mean field theory. We also present the comparison between the energy envelopes measured from the synthetics and their theoretical counterpart provided by the radiative transfer theory and the diffusion approximation. Excellent agreement is found between numerical simulations and theoretical predictions of radiative transfer theory for the mean intensity. The numerical study highlights the difference of attenuation length between the mean field and the mean intensity. In the forward scattering regime, the peak intensity appears to decay exponentially over a length scale known as the transport mean free path. Furthermore, the fluctuations of intensity in the ballistic peak exhibit a transition from Log-normal to Exponential statistics. This transition occurs for a propagation distance of the order of the mean free path, which offers an alternative method of estimating this parameter.https://www.frontiersin.org/articles/10.3389/feart.2022.1033109/fullnumerical simulationrandom mediascatteringcoherent wavefieldscattering attenuationtransport scattering attenuation |
| spellingShingle | Malcon Celorio Malcon Celorio Emmanuel Chaljub Ludovic Margerin Laurent Stehly Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory Frontiers in Earth Science numerical simulation random media scattering coherent wavefield scattering attenuation transport scattering attenuation |
| title | Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory |
| title_full | Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory |
| title_fullStr | Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory |
| title_full_unstemmed | Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory |
| title_short | Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory |
| title_sort | propagation of 2 d sh waves in random media insights from ab initio numerical simulations and transport theory |
| topic | numerical simulation random media scattering coherent wavefield scattering attenuation transport scattering attenuation |
| url | https://www.frontiersin.org/articles/10.3389/feart.2022.1033109/full |
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